Slf-Esteem Scoresdepression Scores
Mean 3.43 15.78
StrdDev 0.75 10.34
13. The above chart contains the means and standard deviations for self-esteem scores and depression scores. Using this information and the most likely correlation coefficient obtained in Question 12 (-.76), what is the regression equation for this data?
a. y = -51.72-10.48x
b. y= -21.45 -1.65x
c. y = 51.72-10.48x
d. y= 21.45 -1.65x
To find the regression equation, we need to use the given information of the means, standard deviations, and the correlation coefficient. The general form of a linear regression equation is y = mx + b, where y is the dependent variable (depression scores), x is the independent variable (self-esteem scores), m is the slope, and b is the y-intercept.
Given that the correlation coefficient obtained is -0.76, we can determine the slope (m) using the formula:
m = (correlation coefficient * standard deviation of y) / standard deviation of x
m = (-0.76 * 10.34) / 0.75
m = -8.8256
Now, to find the y-intercept (b), we can use the formula:
b = mean of y - (m * mean of x)
b = 15.78 - (-8.8256 * 3.43)
b = 15.78 + 30.2917
b = 46.0717
So, the regression equation is:
y = -8.8256x + 46.0717
Comparing this with the given options, the correct answer is:
a. y = -51.72 - 10.48x